Modern introductory physics

Modern Introductory Physics

Charles H. Holbrow • James N. Lloyd

Joseph C. Amato • Enrique Galvez

M. Elizabeth Parks

Modern Introductory Physics

Second Edition

123

ISBN 978-0-387-79079-4 e-ISBN 978-0-387-79080-0

DOI 10.1007/978-0-387-79080-0

Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2010930691

c Springer Science+Business Media, LLC 1999, 2010

All rights reserved. This work may not be translated or copied in whole or in part without the

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Cover: ATM images of O2 molecules and two O atoms courtesy of Dr. Wilson Ho, Donald

Bren Professor of Physics and Chemistry & Astronomy, Department of Physics and Astronomy,

University of California, Irvine.

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Springer is part of Springer Science+Business Media (www.springer.com)

Charles H. Holbrow

Charles A. Dana Professor of Physics,

Emeritus

231 Pearl St.

Cambridge, Massachusetts 02139

USA

[email protected]

James N. Lloyd

Professor of Physics, Emeritus

Colgate University

Department of Physics & Astronomy

37 University Ave.

Hamilton, New York 13346

USA

[email protected]

Joseph C. Amato

William R. Kenan, Jr. Professor of

Physics, Emeritus

Colgate University

Department of Physics & Astronomy

13 Oak Drive

Hamilton, New York 13346

USA

[email protected]

Enrique Galvez

Professor of Physics

Colgate University

Department of Physics & Astronomy

13 Oak Drive

Hamilton, New York 13346

USA

[email protected]

M. Elizabeth Parks

Associate Professor of Physics

Colgate University

Department of Physics & Astronomy

13 Oak Drive

Hamilton, New York 13346

USA

[email protected]

... all things are made of atoms—little particles that move around in

perpetual motion, attracting each other when they are a little distance

apart, but repelling upon being squeezed into one another.

In that one sentence, you will see, there is an enormous amount of

information about the world, if just a little imagination and thinking are

applied.

— Richard P. Feynman

Preface

This book grew out of an ongoing effort to modernize Colgate University’s

three-term, introductory, calculus-level physics course. The book is for the

first term of this course and is intended to help first-year college students

make a good transition from high-school physics to university physics.

The book concentrates on the physics that explains why we believe that

atoms exist and have the properties we ascribe to them. This story line,

which motivates much of our professional research, has helped us limit

the material presented to a more humane and more realistic amount than

is presented in many beginning university physics courses. The theme

of atoms also supports the presentation of more non-Newtonian topics

and ideas than is customary in the first term of calculus-level physics.

We think it is important and desirable to introduce students sooner than

usual to some of the major ideas that shape contemporary physicists’

views of the nature and behavior of matter. Here in the second decade of

the twenty-first century such a goal seems particularly appropriate.

The quantum nature of atoms and light and the mysteries associated

with quantum behavior clearly interest our students. By adding and em￾phasizing more modern content, we seek not only to present some of the

physics that engages contemporary physicists but also to attract students

to take more physics. Only a few of our beginning physics students come

to us sharply focused on physics or astronomy. Nearly all of them, how￾ever, have taken physics in high school and found it interesting. Because

we love physics and believe that its study will open students’ minds to

an extraordinary view of the world and the universe and also prepare

them well for an enormous range of roles—citizen, manager, Wall-Street

broker, lawyer, physician, engineer, professional scientist, teachers of all

kinds—we want them all to choose undergraduate physics as a major.

vii

viii PREFACE

We think the theme and content of this book help us to missionize more

effectively by stimulating student interest. This approach also makes our

weekly physics colloquia somewhat accessible to students before the end

of their first year.1

In parallel with presenting more twentieth-century physics earlier than

is usual in beginning physics, this book also emphasizes the exercise and

development of skills of quantitative reasoning and analysis. Many of our

students come fairly well prepared in both physics and math—an appre￾ciable number have had some calculus—but they are often rusty in basic

quantitative skills. Many quite capable students lack facility in working

with powers-of-ten notation, performing simple algebraic manipulation,

making and understanding scaling arguments, and applying the rudiments

of trigonometry. The frustrations that result when such students are ex￾posed to what we would like to think is “normal discourse” in a physics

lecture or recitation clearly drive many of them out of physics. There￾fore, in this first term of calculus-level physics we use very little calculus

but strongly emphasize problems, order-of-magnitude calculations, and

descriptions of physics that exercise students in basic quantitative skills.

To reduce the amount of confusing detail in the book, we often omit in￾teresting (to the authors) facts that are not immediately pertinent to the

topic under consideration. We also limit the precision with which we treat

topics. If we think that a less precise presentation will give the student

a better intuitive grasp of the physics, we use that approach. For exam￾ple, for the physical quantities mass, length, time, and charge, we stress

definitions more directly connected to perceivable experience and pay lit￾tle attention to the detailed, technically correct SI definitions. This same

emphasis on physical understanding guides us in our use of the history of

physics. Many physical concepts and their interrelations require a histor￾ical framework if they are to be understood well. Often history illustrates

how physics works by showing how we come to new knowledge. But if we

think that the historical framework will hinder understanding, we take

other approaches. This means that although we have tried diligently to

1These and other aspects of the approach of this book are discussed in more detail in C.H. Hol￾brow, J.C. Amato, E.J. Galvez, and J.N. Lloyd, “Modernizing introductory physics,” Am. J.

Phys. 63, 1078–1090 (1995); J.C. Amato, E.J. Galvez, H. Helm, C.H. Holbrow, D.F. Holcomb,

J.N. Lloyd and V.N. Mansfield, “Modern introductory physics at Colgate,” pp. 153–157, Con￾ference on the Introductory Physics Course on the Occasion of the Retirement of Robert

Resnick, edited by Jack Wilson, John Wiley & Sons, Inc., New York, 1997; C.H. Holbrow and

J.C. Amato, “Inward bound/outward bound: modern introductory physics at Colgate,” in The

Changing Role of Physics Departments in Modern Universities, pp. 615–622, Proceedings of In￾ternational Conference on Undergraduate Physics Education, College Park, Maryland, August

1996, edited by E.F. Redish and J.S. Rigden, AIP Conference Proceedings 399, Woodbury,

New York, 1997.

PREFACE ix

avoid saying things that are flat out historically wrong, we do subordinate

history to our pedagogical goals.

We believe that it is important for students to see how the ideas of

physics are inferred from data and how data are acquired. Clarity and

concision put limits on how much of this messy process beginning students

should be exposed to, but we have attempted to introduce them to the

realities of experimentation by including diagrams of apparatus and tables

of data from actual experiments. Inference from tables and graphs of data

is as important a quantitative skill as the others mentioned above.

Asking students to interpret data as physicists have (or might have)

published them fits well with having beginning physics students use com￾puter spreadsheets to analyze data and make graphical displays. Because

computer spreadsheets are relatively easy to learn and are widely used

outside of physics, knowledge of them is likely to be useful to our stu￾dents whether they go on in physics or not. Therefore, we are willing to

have our students take a little time from learning physics to learn to use a

spreadsheet package. Some spreadsheet exercises are included as problems

in this book.

The examination of significant experiments and their data is all very

well, but nothing substitutes for actual experiences of observation and

measurement. The ten or so laboratory experiments that we have devel￾oped to go along with this course are very important to its aims. This is

particularly so, since we observe that increasingly our students come to

us with little experience with actual physical phenomena and objects. We

think it is critically important for students themselves to produce beams

of electrons and bend them in magnetic fields, to create and measure in￾terference patterns, to observe and measure electrolysis, etc. Therefore,

although we believe our book will be useful without an accompanying

laboratory, it is our heartfelt recommendation that there be one.

Although our book has been developed for the first of three terms of in￾troductory physics taken by reasonably well-prepared and well-motivated

students, it can be useful in other circumstances. The book is particularly

suitable for students whose high-school physics has left them with a desire

to know more physics, but not much more. For them a course based on

this book can stand alone as an introduction to modern physics. The book

can also work with less well prepared students if the material is spread

out over two terms. Then the teacher can supplement the coverage of the

material of the first several chapters and build a solid foundation for the

last half of the book.

x PREFACE

The format and techniques in which physics is presented strongly affect

student learning. In teaching from this book we have used many inno￾vative pedagogical ideas and techniques of the sort vigorously presented

over many years by well-known physics pedagogues such as Arnold Arons,

Lillian McDermott, Priscilla Laws, Eric Mazur, David Hestenes, and Alan

van Heuvelen. In one form or another they emphasize actively engaging

the students and shaping instruction in such a way as to force students

to confront, recognize, and correct their misconceptions. To apply these

ideas we teach the course as two lectures and two small-group recita￾tions each week. In the lectures we use Mazur-style questions; in the

recitations we have students work in-class exercises together; we spend

considerable effort to make exams and special exercises reach deeper than

simple numerical substitution.

Drawing on more than ten years of experience teaching from Modern

Introductory Physics, we have significantly revised it. Our revisions correct

errors in the 1999 edition and provide clearer language and more complete

presentation of important concepts. We have also reordered the chapters

on the discovery of the nucleus, the Bohr model of the atom, and the

Heisenberg uncertainty principle to better tell the story of the ongoing

discovery of the atom.

Our boldest innovation is the addition of two chapters on basic features

of quantum mechanics. In the context of real experiments, these chap￾ters introduce students to some of the profoundly puzzling consequences

of quantum theory. Chapter 19 introduces superposition using Richard

Feynman’s approach; Chap. 20 discusses quantum entanglement, the vi￾olation of Bells inequalities, and experiments that vindicate quantum

mechanics. Superposition, entanglement, non-locality, and Bell’s inequal￾ities are part of the remarkable success story of quantum mechanics. We

want acquaintance with these important ideas to alert students to themes

and technologies of twenty-first century physics. We want our book, which

unfolds the ideas and discoveries that led to the quantum revolution, to

end by opening for students a window into a future shaped by themes and

emerging technologies that rely fundamentally on quantum mechanics.

Many colleagues helped us make this a more effective book with their

useful critiques, problems, exercises, insights, or encouragement. For these

we are grateful to Victor Mansfield (1941–2008), Hugh Helm (1931–2007),

Shimon Malin, Stephen FitzGerald, Scott Lacey, Prabasaj Paul, Kurt

Andresen, Pat Crotty, Jonathan Levine, Jeff Buboltz, and Ken Segall.

Deciding what specific subject matter should go into beginning physics

has been a relatively small part of the past 30 years’ lively discussions

of pedagogical innovation in introductory physics. We hope our book will

help to move this important concern further up the agenda of physics

teachers. We think the content and subject emphases of introductory

PREFACE xi

physics are a central responsibility of physics teachers and of great

importance to the long-term health of the physics community. This

book represents our idea of a significant step toward making introduc￾tory physics better represent what physics is. Whether or not we have

succeeded, we hope this book will stimulate discussion about, encour￾age experimentation with, and draw more attention to the content of

undergraduate introductory physics.

Charles H. Holbrow

James N. Lloyd

Joseph C. Amato

Enrique Galvez

M. Elizabeth Parks

Colgate University

August, 2010

Contents

1 What’s Going On Here? 1

1.1 What Is Physics? ............................. 1

1.2 What Is Introductory Physics About? ................. 3

1.3 What We’re Up To ............................ 4

1.4 This Course Tells a Story ........................ 5

The Short Story of the Atom ................... 5

Special Relativity and Quantum Mechanics ........... 7

Physics Is Not a Spectator Sport ................. 7

1.5 Why This Story? ............................. 9

An Important Idea ......................... 9

Tools for Quantitative Thought . . . . . . . . . . . . . . . . . 10

An Introduction to Physics . . . . . . . . . . . . . . . . . . . . 10

1.6 Just Do It! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Some Physics You Need to Know 13

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Length, Mass, Time: Fundamental Physical Properties . . . . . . . 13

Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Some Important Masses, Lengths, and Times . . . . . . . . . 20

2.3 Units and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Composite Units . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Using SI Multipliers . . . . . . . . . . . . . . . . . . . . . . . . 22

Consistency of Units . . . . . . . . . . . . . . . . . . . . . . . . 24

Physical Dimensions . . . . . . . . . . . . . . . . . . . . . . . . 25

xiii

xiv CONTENTS

2.4 Angles and Angular Measure . . . . . . . . . . . . . . . . . . . . . . 26

Vertex and Rays . . . . . . . . . . . . . . . . . . . . . . . . . . 27

What Does “Subtend” Mean? . . . . . . . . . . . . . . . . . . 27

Degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

More About the Small-Angle Approximation . . . . . . . . . . 30

2.5 Thinking About Numbers . . . . . . . . . . . . . . . . . . . . . . . . 32

2.6 Momentum, Force, and Conservation of Momentum . . . . . . . . . 35

Velocity and Acceleration . . . . . . . . . . . . . . . . . . . . . 35

Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Why Does F = ma? . . . . . . . . . . . . . . . . . . . . . . . . 39

Conservation of Momentum . . . . . . . . . . . . . . . . . . . . 40

Centripetal Forces . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.7 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Feynman’s Energy Analogy . . . . . . . . . . . . . . . . . . . . 45

Energy Costs Money . . . . . . . . . . . . . . . . . . . . . . . . 47

Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . 47

Pendulums and Energy . . . . . . . . . . . . . . . . . . . . . . 51

Forces As Variations in Potential Energy . . . . . . . . . . . . 53

2.8 Summary and Exhortations . . . . . . . . . . . . . . . . . . . . . . . 54

Connect Concepts to Physical Reality . . . . . . . . . . . . . . 54

Know the SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . 55

Representing Vectors . . . . . . . . . . . . . . . . . . . . . . . . 56

Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Adding Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3 The Chemist’s Atoms 63

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.2 Chemical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3 Atoms and Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Proust’s Evidence: The Law of Constant Proportions . . . . . 65

Dalton’s Evidence: The Law of Multiple Proportions . . . . . 65

Gay-Lussac’s Evidence: The Law of Combining Volumes . . . 67

Avogadro’s Principle . . . . . . . . . . . . . . . . . . . . . . . . 69

3.4 Atomic Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.5 Numbers of Atoms in a Sample . . . . . . . . . . . . . . . . . . . . 74

The Mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Avogadro’s Constant . . . . . . . . . . . . . . . . . . . . . . . . 75

3.6 The Chemist’s Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

CONTENTS xv

4 Gas Laws 83

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

The Idea of Pressure . . . . . . . . . . . . . . . . . . . . . . . . 83

Definition of Pressure . . . . . . . . . . . . . . . . . . . . . . . 85

Discovery of Vacuum and the Atmosphere . . . . . . . . . . . 85

Gas Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.3 Boyle’s Law: The Springiness of Gases . . . . . . . . . . . . . . . . 89

Boyle’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . 89

4.4 Temperature, Gases, and Ideal Gases . . . . . . . . . . . . . . . . . 94

Thermal Expansion . . . . . . . . . . . . . . . . . . . . . . . . 94

Imagining an Ideal Gas . . . . . . . . . . . . . . . . . . . . . . 99

Gay-Lussac’s Law and the Kelvin Temperature Scale . . . . . 100

4.5 The Ideal Gas Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

What Underlies Such a Simple Law? . . . . . . . . . . . . . . 104

5 Hard-Sphere Atoms 109

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.2 Gas Pressure from Atoms . . . . . . . . . . . . . . . . . . . . . . . . 110

5.3 Temperature and the Energies of Atoms . . . . . . . . . . . . . . . 115

Energies of Atoms: Boltzmann’s Constant . . . . . . . . . . . 116

The Electron Volt (eV) . . . . . . . . . . . . . . . . . . . . . . 118

5.4 Summary Thus Far . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.5 Size of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Colliding Atoms, Mean Free Path . . . . . . . . . . . . . . . . 122

Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

An Atomic Model of Viscosity . . . . . . . . . . . . . . . . . . 127

5.7 The Size of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Radius of a Molecule . . . . . . . . . . . . . . . . . . . . . . . . 132

Avogadro’s Number . . . . . . . . . . . . . . . . . . . . . . . . 133

5.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Sums and the Notation . . . . . . . . . . . . . . . . . . . . 136

Distributions and Averages . . . . . . . . . . . . . . . . . . . 137

A Distribution of Velocities . . . . . . . . . . . . . . . . . . . . 140

Momentum Transfers by Collision . . . . . . . . . . . . . . . . 140

Velocity Bins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6 Electric Charges and Electric Forces 151

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.2 Electric Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Experiments with Electroscopes . . . . . . . . . . . . . . . . . 152

Conductors and Insulators . . . . . . . . . . . . . . . . . . . . 157

Quantitative Measures of Charge . . . . . . . . . . . . . . . . . 157